Automated anesthesia promises to enable more precise and personalized anesthetic administration and free anesthesiologists from repetitive tasks, allowing them to focus on the most critical aspects of a patient's surgical care. Current research has typically focused on creating simulated environments from which agents can learn. These approaches have demonstrated good experimental results, but are still far from clinical application. In this paper, Policy Constraint Q-Learning (PCQL), a data-driven reinforcement learning algorithm for solving the problem of learning anesthesia strategies on real clinical datasets, is proposed. Conservative Q-Learning was first introduced to alleviate the problem of Q function overestimation in an offline context. A policy constraint term is added to agent training to keep the policy distribution of the agent and the anesthesiologist consistent to ensure safer decisions made by the agent in anesthesia scenarios. The effectiveness of PCQL was validated by extensive experiments on a real clinical anesthesia dataset. Experimental results showthat PCQL is predicted to achieve higher gains than the baseline approach while maintaining good agreement with the reference dose given by the anesthesiologist, using less total dose, and being more responsive to the patient's vital signs. In addition, the confidence intervals of the agent were investigated, which were able to cover most of the clinical decisions of the anesthesiologist. Finally, an interpretable method, SHAP, was used to analyze the contributing components of the model predictions to increase the transparency of the model.